Flight computer systems &amp; methods to determine airspeed

ABSTRACT

According to one implementation of the present disclosure, a method for determining airspeed for an unpowered vehicle is disclosed. The method includes: during flight, determining, by an accelerometer disposed on the unpowered vehicle, first and second accelerometer outputs, where the first and second accelerometer outputs correspond to respective first and second body-fixed load factor measurements; determining an angle-of-attack parameter; determining a body Z-force coefficient based on the angle-of-attack parameter; and determining an airspeed value based on the second body-fixed load factor measurement and the second body-fixed coefficient.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

BACKGROUND

This section is intended to provide background information to facilitate a better understanding of various technologies described herein. As the section's title implies, this is a discussion of related art. That such art is related in no way implies that it is prior art. The related art may or may not be prior art. It should therefore be understood that the statements in this section are to be read in this light, and not as admissions of prior art.

In aerospace applications, airspeed may be required for optimal performance of a small vehicle (such as a glider). For such small vehicles, accurate estimation and/or measuring of airspeed can be difficult to ascertain due to the size of the required probe with respect to the size of the vehicle or the weight and expense of obtaining the inertial measurements necessary for accurate estimation.

Current methods to determine airspeed include direct measurement and/or estimation based on the fusion of precise position and inertial measurements. However, these methods require the use of external probes and/or system components that may be prohibitively expensive and/or may not be possible due to size or weight constraints relative to the intended application.

SUMMARY

According to one implementation of the present disclosure, a method for determining airspeed for an unpowered is disclosed. The method includes: during flight, determining, by an accelerometer disposed on the unpowered vehicle, first and second accelerometer outputs, where the first and second accelerometer outputs correspond to respective first and second body-fixed load factor measurements; determining an angle-of-attack parameter; determining a body Z-force coefficient based on the angle-of-attack parameter; and determining an airspeed value based on the second body-fixed load factor measurement and the second body-fixed coefficient.

According to another implementation of the present disclosure, a flight computer system (i.e., computer, flight control system) is disclosed. The flight control system includes a processor and a memory accessible to the processor. The memory stores instructions that are executable by the processor to perform operations including: during flight, determining, by an accelerometer disposed on the unpowered vehicle, first and second accelerometer outputs, where the first and second accelerometer outputs correspond to respective first and second body-fixed load factor measurements; determining an angle-of-attack parameter; determining a body Z-force coefficient based on the angle-of-attack parameter; and determining an airspeed value based on the second body-fixed load factor measurement and the second body-fixed coefficient.

According to another implementation of the present disclosure, a non-transitory computer-readable storage device storing instructions that, when executed by a processor, cause the processor to: during flight, determining, by an accelerometer disposed on the unpowered vehicle, first and second accelerometer outputs, where the first and second accelerometer outputs correspond to respective first and second body-fixed load factor measurements; determining an angle-of-attack parameter; determining a body Z-force coefficient based on the angle-of-attack parameter; and determining an airspeed value based on the second body-fixed load factor measurement and the second body-fixed coefficient.

The above-referenced summary section is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description section. Additional concepts and various other implementations are also described in the detailed description. The summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter, nor is it intended to limit the number of inventions described herein. Furthermore, the claimed subject matter is not limited to implementations that solve any or all disadvantages noted in any part of this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The present technique(s) will be described further, by way of example, with reference to embodiments thereof as illustrated in the accompanying drawings. It should be understood, however, that the accompanying drawings illustrate only the various implementations described herein and are not meant to limit the scope of various techniques, methods, systems, or apparatuses described herein.

FIG. 1 illustrates a side view of a vehicle in accordance with implementations of various techniques described herein.

FIG. 2 illustrates a graphical representation in accordance with implementations of various techniques described herein.

FIG. 3 illustrates a graphical representation in accordance with implementations of various techniques described herein.

FIG. 4 illustrates a graphical representation in accordance with implementations of various techniques described herein.

FIG. 5 illustrates a graphical representation in accordance with implementations of various techniques described herein.

FIG. 6 illustrates a graphical representation in accordance with implementations of various techniques described herein.

FIG. 7 illustrates a graphical representation in accordance with implementations of various techniques described herein.

FIG. 8 illustrates a graphical representation in accordance with implementations of various techniques described herein.

FIG. 9 illustrates a graphical representation in accordance with implementations of various techniques described herein.

FIG. 10 illustrates a graphical representation in accordance with implementations of various techniques described herein.

FIG. 11 illustrates a graphical representation in accordance with implementations of various techniques described herein.

FIG. 12 illustrates a graphical representation in accordance with implementations of various techniques described herein.

FIG. 13 illustrates a graphical representation in accordance with implementations of various techniques described herein.

FIG. 14 is a particular illustrative aspect of methods in accordance with implementations of various techniques described herein.

FIG. 15 is a particular illustrative aspect of methods in accordance with implementations of various techniques described herein.

FIG. 16 is a block diagram of a computer system in accordance with implementations of various techniques described herein.

Reference is made in the following detailed description to accompanying drawings, which form a part hereof, wherein like numerals may designate like parts throughout that are corresponding and/or analogous. It will be appreciated that the figures have not necessarily been drawn to scale, such as for simplicity and/or clarity of illustration. For example, dimensions of some aspects may be exaggerated relative to others. Further, it is to be understood that other embodiments may be utilized. Furthermore, structural and/or other changes may be made without departing from claimed subject matter. References throughout this specification to “claimed subject matter” refer to subject matter intended to be covered by one or more claims, or any portion thereof, and are not necessarily intended to refer to a complete claim set, to a particular combination of claim sets (e.g., method claims, apparatus claims, etc.), or to a particular claim. It should also be noted that directions and/or references, for example, such as up, down, top, bottom, and so on, may be used to facilitate discussion of drawings and are not intended to restrict application of claimed subject matter. Therefore, the following detailed description is not to be taken to limit claimed subject matter and/or equivalents.

DETAILED DESCRIPTION

Advantageously, systems and methods of the present disclosure allow for the determination of an airspeed value (and in some implementations, aerodynamic angle-of-attack (AOA) parameter corresponding to a particular AOA orientation angle) without the use of a pitot-static system including pitot-static probes (e.g., tubes, cones, vanes, etc.) having relatively bulky and/or heavy sensors. In addition, in contrast to conventional methods, because such probes are not required for measurement, estimation, and/or computer process, advantageously, the airspeed for a gliding vehicle (i.e., an unpowered vehicle) can be determined directly with the utilization of a flight computer system and an accelerometer disposed on the gliding vehicle. In example implementations, gliding vehicles include, but are not limited to, sailplanes, meteorological or battle damage assessment gliders, gliding submunitions, model airplanes, or any similar flight vehicle not under direct power (e.g., a general aviation aircraft gliding with power off/engine out).

In certain aspects, the airspeed of an unpowered vehicle may be determined when the AOA parameter is already known through some other means, but a pitot-static system/probes is not desirable or available. In other implementations, both of the airspeed and AOA parameter can be determined without the use of a pitot-static system/probes. Thus, advantageously, the airspeed of an unpowered vehicle may be determined without regard to how the AOA parameter is determined.

As a further advantage, the present disclosure allows for the capacity of an airspeed flight computer system to generate a flight profile of the unpowered vehicle. Also, in certain inventive aspects, the present disclosure allows for the capacity of a flight computer system to estimate (i.e., compute) for winds in optimizing trajectory for vehicle guidance algorithms. Additionally, the airspeed flight control system may be used as an auxiliary system to determine airspeed. Also, the airspeed flight computer system (utilizing a closed-loop control system) may determine and correct (i.e., adjust) for airspeed (in combination with AOA orientation in certain implementations) of the unpowered vehicle to an airspeed (in combination with AOA orientation in certain implementations) having the most advantageous lift-to-drag (i.e., lift-to-drag ratio, L/D) for maximum distance coverage.

FIG. 1 illustrates a side view of an unpowered vehicle 100 (e.g., small glider, vehicle) during flight according to one implementation. As shown, the unpowered vehicle 100 may travel along a velocity vector 110 (where the magnitude of velocity vector corresponds to an airspeed (i.e., airspeed value)). As the unpowered vehicle 100 is traveling, various force vectors are shown to be enacted. These force vectors include: a normal force 120 (due to pressure on the surface of the vehicle 100), a lift force 130, a drag force 140, an axial force 150, and weight. As shown in FIG. 1, in contrast to the normal force and axial force vectors (which are “body-fixed”), lift and drag force vectors are not “body-fixed” and are normal and parallel, respectively, to the velocity vector 110. Moreover, X and Z-directions represent X and Z-body-axes of a body-axes coordinate system.

As further illustrated, referring to the pitch axis, when the vehicle 100 points to a particular direction of flight, the force vectors may be expressed with respect to the incidence angle (α). Utilizing these applied forces, an accelerometer 115 may be used during flight to measure first and second body-fixed load factor components (N_(X) and N_(Z)) (i.e., first and second body-fixed load factors, first and second body-axes load factors). In certain implementations, the accelerometer 115 may be located on the vehicle 100 at the center of gravity (CG) of the vehicle 100 or may be mathematically-corrected to the center of gravity of the vehicle 100.

As an example, the first body-fixed load factor component, N_(X) (i.e., first accelerometer output) is expressed as a quotient of a magnitude of axial force and weight, while the second body-fixed load factor component, N_(Z) (i.e., second accelerometer output) is expressed as a quotient of a magnitude of normal force and weight. Moreover, as utilized in the inventive systems and methods (as described herein), the quotient of the first and second body-fixed load factor components (N_(X) and N_(Z)) may be substantially equivalent to a quotient of a particular first and second body-fixed coefficients (C_(X) and C_(Z)) (as described in below paragraphs):

Hence,

$\frac{Nx}{Nz} = {\frac{Cx}{Cz}.}$

Advantageously, in certain implementations, this relationship is utilized in the inventive systems and methods as described herein. For example, in certain implementations, the airspeed value (V) (i.e., the magnitude of the velocity vector 110) may be computed through the following equation (as described in below paragraphs):

$v = {\left( \frac{2\mspace{14mu} {Nz}\mspace{14mu} ({Weight})}{\rho \mspace{14mu} {Sref}\mspace{14mu} {Cz}} \right)^{\frac{1}{2}}.}$

In the equation, N_(Z) corresponds to second body-fixed load factor measurement; Weight corresponds to mass*gravity; p corresponds to air density; Sref corresponds to reference wing area; and C_(Z) corresponds to the body Z-force coefficient (i.e., second body-fixed coefficient).

In some implementations, a desired flight profile for the vehicle 100 may include settings for the vehicle 100 to operate at angle-of-attack orientation and airspeed allowing for the greatest lift-to-draft (L/D) for maximum distance coverage. The L/D term (i.e., L/D ratio) may be computed for a particular airspeed by measuring the lift generated in comparison with the drag at that speed. For calculation purposes, the lift-to-draft ratio may be determined by dividing the lift coefficient C_(L) by the drag coefficient C_(D).

For the following graphical representations (FIGS. 2-16) of the systems and methods described herein, an aircraft may dispense the vehicle 100 (e.g., a small glider) for damage assessment. In other cases, the vehicle 100 may perform weather measurements, various military operations (including weapons deployment), etc. In the example, the vehicle 100 includes a weight of 1-pound, a wingspan of 16-inch, and a 2-inch wing-chord. For each of the graphical representations (200-1600), the Y-component ranges may vary depending upon weight, wingspan, and wing-chord characteristics of the particular vehicle.

In FIG. 2, graph 200 illustrates estimated drag coefficient curves for three elevator deflection settings (de): −5, 0, and 5. As shown, graph 200 includes an expected range for drag, as represented as drag coefficient values C_(D) (from 0 to 0.35) for the vehicle 100 (on the Y-axis) 210, as a function of a range of angle-of-attack directions (from −5° to 20°) (on the X-axis) 220. In certain implementations, the drag coefficient C_(D) is a dimensionless quantity that may be used to quantify the drag or resistance of the vehicle 100 in a fluid environment, such as air or water.

In FIG. 3, graph 300 illustrates estimated lift coefficient curves for the three elevator deflection settings (de): −5, 0, and 5. As shown, graph 300 includes an expected range for lift, as represented as lift coefficient values C_(L) (from −2 to 1.6), for the vehicle 100 (on the Y-axis) 310, as a function of the range of angle-of-attack directions (from −5° to 20°) (on the X-axis) 320. In certain implementations, the lift coefficient C_(L) is a dimensionless quantity that may be used to quantify the lift generated by the vehicle 100 to the fluid density around the vehicle 100, the fluid velocity, and an associated foil chord of the vehicle 100.

In certain implementations, the lift and drag coefficient values are aerodynamic data characteristics (i.e., values, metrics, first and second aerodynamic data values) that may be obtained by estimating the range of body-fixed accelerations C_(X)/C_(Z) (as described in below paragraphs) for the vehicle 100 or by measuring wind tunnel data with respect to the vehicle 100.

FIGS. 4 and 5 illustrate the drag coefficient values C_(D) and lift coefficient values C_(L) transformed to body-fixed coefficients: body X-force coefficient (i.e., first body-fixed coefficient) and body Z-force coefficient C_(Z) (i.e., second body-fixed coefficient), respectively. In one implementation, the first and second body-fixed coefficients C_(X) and C_(Z) may be determined through computation of the following equations:

C _(X) =−C _(D) cos α+C_(L) sin α

C _(Z) =−C _(L) cos α−C_(D) sin α

In FIG. 4, graph 400 illustrates the body X-force coefficient (i.e., the first body-fixed coefficient) for the three elevator deflection settings (de): −5, 0, and 5. As shown, graph 400 includes a range of body X-force coefficients (from −0.05 to 0.2) (on the Y-axis) 410 as a function of the range of angle-of-attack directions (from −5° to 20°) (on the X-axis) 420.

In FIG. 5, graph 500 illustrates the body Z-force coefficient (i.e., C_(Z), the second body-fixed coefficient) for the three elevator deflection settings (de): −5, 0, and 5. As shown, graph 500 includes a range of body Z-force coefficients (from −1.6 to 0.2) (on the Y-axis) 510 as a function of the range of angle-of-attack directions (from −5° to 20° (on the X-axis) 520. Advantageously, the example graph can be utilized for table lookup to determine C_(Z) (when an AOA is known for airspeed computation (in accordance with the method 1500)) based on elevator deflections.

In FIG. 6, graph 600 illustrates the C_(X)/C_(Z) ratio for the three elevator deflection settings (de): −5, 0, and 5. As shown, graph 600 includes the C_(X)/C_(Z) ratio (from −8 to 4) (on the Y-axis) 610 as a function of the range of angle-of-attack directions (from −5° to 20° (on the X-axis) 620. Notably, a collapse may be seen on the graph curvature (C_(X)/C_(Z) ratio plot points over a range of usable angle-of-attack) for the “0” elevator deflection setting.

In FIG. 7, graph 700 illustrates a portion of the C_(X)/C_(Z) ratio for the “0” elevator deflection setting (de=0) from FIG. 6. As shown, graph 700 (i.e., an angle-of-attack operating plot, angle-of-attack operating map, angle-of-attack look-up plot) includes the C_(X)/C_(Z) ratio (from −0.5 to ⅗) (on the Y-axis) 710 as a function of the range of angle-of-attack directions (from −5° to 20° (on the X-axis) 720. Notably, a monotonic portion 740 (of the C_(X)/C_(Z) ratio as a function of the range of angle-of-attack directions) of a C_(X)/C_(Z) look-up curve 730 (i.e., a monotonic curve, body-fixed accelerations curve) (e.g., a portion of the curvature 730 that does not increase) can serve as a look-up curve (i.e., a look-up table) or be applied in curve-fitting for a range (i.e., a plurality) of prospective (i.e., possible, useful) angle of attack operating points. In one implementation, a particular operating point on the monotonic portion may be determined by applying a quotient of the first and second accelerometer outputs (i.e., N_(X)/N_(Z)) to the angle-of-attack operating (look-up) plot 700. For instance, this may be applied by matching a quotient of the first and second accelerometer outputs (N_(X)/N_(Z)) to a substantially equivalent body-fixed acceleration (C_(X)/C_(Z)), where the body-fixed acceleration (C_(X)/C_(Z)) may correspond to a particular quotient of a particular first and second body-fixed coefficients (C_(X), C_(Z)). Upon matching

${\frac{Nx}{Nz} = \frac{Cx}{Cz}},$

a computer system (e.g., such as any of the computers in flight computer system 1600) may determine an angle-of-attack parameter that corresponds to the determined operating point.

Accordingly, in the example methods, after the drag coefficient values C_(D) and the lift coefficient values C_(L) are transformed into respective components of the first and second body-fixed coefficients C_(X) and C_(Z), a C_(X)/C_(Z) ratio (i.e., a body-fixed acceleration) may be used to establish the monotonic portion 740 for angle-of-attack look-up. Moreover, measured accelerometer components N_(X) and N_(Z) may be divided and matched on a monotonic portion of a lookup curve on a plot comparing body-fixed accelerations to prospective AOA parameters. Further, an operating point that aligns to the Y-axis may be used to determine where on the X-axis (of prospective AOA parameters) alignment takes place.

In FIG. 8, graph 800 illustrates a lift-to-drag ratio C_(L)/C_(D) for the three elevator deflection settings (de): −5, 0, and 5. As shown, graph 800 includes the lift-to-drag ratio C_(L)/C_(D) (from −5 to 15) (on the Y-axis) 810 as a function of the range of angle-of-attack directions (from −5° to 20°) (on the X-axis) 820. Notably, provided on lift-to-drag ratio C_(L)/C_(D) curves 830, graph 800 depicts the respective operating points 834 (for the three elevator deflection settings) and the corresponding AOA parameter 836 for selection of an ideal angle-of-attack operating point, if an optimal lift-to-drag ratio is to be prioritized. In such an example, the angle-of-attack parameter corresponds to a lift-to-drag-optimized angle-of-attack.

In FIG. 9, graph 900 illustrates a lift-to-drag C_(L) ^(3/2/C) _(D) ratio (i.e., a second lift-to-drag ratio) for the three elevator deflection settings (de): −5, 0, and 5. As shown, graph 900 includes the second lift-to-drag C_(L) ^(3/2)/C_(D) ratio (from 0 to 14) (on the Y-axis) 910 as a function of the range of angle-of-attack directions (from −5° to 20°) (on the X-axis) 920. Notably, graph 900 depicts the respective operating points 934 (for the provided deflection settings) and the corresponding AOA parameter 936 selection if a minimum power point (i.e., a minimum sink rate) is to be prioritized. In such an example, the angle-of-attack parameter corresponds to a minimum-sink rate-optimized angle of attack. In other examples, a combination of two criteria (lift-to-drag and minimum sink-rate) may be used in evaluation for an optimal AOA.

In FIG. 10, graph 1000 illustrates a trimmed body Z-force coefficient (i.e., second body-fixed coefficient) (C_(Z) Trim) curve (dotted-line) 1040 with untrimmed second body-fixed coefficient curves for the elevator deflection settings (de): −5, 0, and 5 (corresponding with FIG. 5). As shown, graph 1000 includes C_(Z) (from −1.4 to 0.2) (on the Y-axis) 1010 as a function of the range of angle-of-attack directions (from −5° to 20° 1020. Advantageously, the C_(Z) trim curve 1040 illustrates the variations of an example curve based on a trim for zero moment through the AOA range at a particular center of gravity (cg) location. In some implementations, for example, the C_(Z) trim curve 1040 can be utilized for table lookup in determining C_(Z) (when the AOA is known) for airspeed computation (in accordance with the method 1500).

FIGS. 11-13 illustrate time history results of a six-degree-of-freedom flight simulation of the vehicle 100 capturing 7° angle-of-attack to operate near maximum lift-to-drag. In FIG. 11, graph 1100 includes angle of attack (from 3.5° to 7° (on the Y-axis) 1110 as a function of time (0-200 seconds) (on the X-axis) 1120. The angle-of-attack comparison shows the comparison of a simulation vehicle angle-of-attack (as shown as the solid-line in FIG. 11) with the estimated angle-of-attack (as shown as the dotted-line in FIG. 11), according to examples as described herein. The estimated angle-of-attack shown is the result of using the ratio N_(X)/N_(Z) from the body-fixed accelerations (i.e., C_(X)/C_(Z)) as input to a table look-up of the monotonic portion of the body-fixed accelerations (i.e., C_(X)/C_(Z)) curve as discussed with reference to FIG. 7 above. Additionally, in FIG. 12, graph 1200 illustrates Lift/Drag ratio (from 0-12.4) (on the Y-axis) 1210 as a function of time (0-200 seconds) (on the X-axis) 1220. Moreover, in FIG. 13, graph 1300 depicts an example airspeed simulation compared to an estimated airspeed using example computation methods as described herein (e.g., with reference to FIG. 14 below). Graph 1300 includes airspeed (from approximately 0 to 50 knots) (on the Y-axis) 1310 as a function of time (0-200 seconds) (on the X-axis) 1320. Notably, as shown in FIG. 15, similar results would be achieved whether trimmed (dotted-line) or untrimmed (dashed-line) versions of the second body-fixed coefficient versus AOA curve(s) may be used depending upon the look-up table formulation.

Referring to FIG. 14, a method 1400 (e.g., implemented as an AOA optimization program 1624) for determining angle-of-attack for an unpowered vehicle 100 applicable for the flight computer system 1600 (as described with reference to FIG. 16) is shown.

At block 1410, the method 1400 includes determining a monotonic portion of a look-up curve of an angle-of-attack operating plot. For example, in certain implementations, with reference to FIG. 7, a monotonic portion 740 of a look-up curve 730 (i.e., a monotonic curve, table look-up; body-fixed accelerations curve) of an angle-of-attack operating plot 700 may be determined (i.e., identified, generated). In some implementations, a monotonic portion 740 of a look-up curve 730 of an angle-of-attack operating plot 700, may be generated prior to an implementation of the method 1200 in any computer either networked to or outside of the computer system 1600, and in other implementations, a monotonic portion 740 of a look-up curve 730 of an angle-of-attack operating plot 700, may be performed concurrently (i.e., in real-time) in any computer networked to the computer system 1600 as part of the method 1400.

As discussed with reference to FIGS. 2-7 (in above paragraphs), determining a monotonic portion of a look-up curve of an angle-of-attack operating plot may include the following steps: (1) obtaining pluralities of first and second aerodynamic data characteristics (i.e., first and second aerodynamic data values) that may be obtained by estimating the range of body-fixed accelerations C_(X)/C_(Z) or by measuring wind tunnel data with respect to the vehicle 100) as respective functions of a range of angle-of-attack directions; (2) computing, by a processor (e.g., a microcontroller, onboard flight control processing device), pluralities of first and second body-fixed coefficients (C_(X) and C_(Z)) as the respective functions of the range of angle-of-attack directions; (3) determining, by the processor, a plurality of body-fixed accelerations (i.e., C_(X)/C_(Z)) as a function of a prospective range of the range of angle-of-attack directions based on respective pluralities of quotients of the first and second body-fixed coefficients as the respective functions of the range of angle-of-attack directions, where the determined plurality of body-fixed accelerations (i.e., C_(X)/C_(Z)) as a function of a prospective range of the range of angle-of-attack directions corresponds to the look-up curve of the angle-of-attack operating plot; and (4) determining the monotonic portion based on a filtering, by the processor, of the look-up curve.

At block 1420, the method 1400 includes during flight, determining, by an accelerometer disposed on the unpowered vehicle, first and second accelerometer outputs, where the first and second accelerometer outputs correspond to first and second body-fixed load factor measurements, respectively. For example, as described with reference to FIG. 1, first and second body-fixed load factor measurements (N_(X) and N_(Z)) can be measured with the aid of an accelerometer 115 disposed on the unpowered vehicle 100.

At block 1430, the method 1400 includes determining an operating point on the monotonic portion by applying a quotient of the first and second accelerometer outputs to the angle-of-attack operating plot. For example, as described with reference to FIGS. 1 and 7, a particular operating point on the monotonic portion 740 may be determined by applying a quotient of the first and second accelerometer outputs (i.e., N_(X)/N_(Z)) to the angle-of-attack operating plot 700.

In one implementation, in block 1430, the method 1400 is carried out by matching a quotient of the first and second accelerometer outputs (N_(X)/N_(Z)) to a substantially equivalent body-fixed acceleration (C_(X)/C_(Z)), where the body-fixed acceleration (C_(X)/C_(Z)) may correspond to a particular quotient of a particular first and second body-fixed coefficients (C_(X), C_(Z)).

At block 1440, the method 1400 includes determining an angle-of-attack parameter corresponding to the determined operating point. For example, as discussed with reference with FIG. 7, upon matching

${\frac{Nx}{Nz} = \frac{Cx}{Cz}},$

a computer system (e.g., such as any computer of computer system 1600) may determine an angle-of-attack parameter that corresponds to the determined operating point.

The method 1400 include further steps such as: in response to determining the angle-of-attack parameter, at least one of: (1) generating, at least partially by a flight computer system, a flight profile of the unpowered vehicle; and (2) adjusting (i.e., correcting), at least partially by the flight computer system (and a closed-loop system), an angle-of-attack setting of the unpowered vehicle based on the angle-of-attack parameter.

Referring to FIG. 15, an example method 1500 (e.g.,implemented as an airspeed program 1626) for determining airspeed for an unpowered vehicle 100 applicable for the flight computer system 1600 (as described with reference to FIG. 16) is shown.

At block 1510, the method 1500 includes during flight, determining, by an accelerometer disposed on the unpowered vehicle, first and second accelerometer outputs, where the first and second accelerometer outputs correspond to first and second body-fixed load factor measurements, respectively. For example, as described with reference to FIG. 1, first and second body-fixed load factor measurements (N_(X) and N_(Z)) can be measured with the aid of an accelerometer 115 disposed on the unpowered vehicle 100.

At block 1520, the method 1500 includes determining an angle-of-attack parameter. For example, in certain implementations, with reference to FIG. 14, and angle-of-attack parameter may be determined via computation and/or formulation (i.e., AOA optimization program).

At block 1530, the method 1500 includes determining a body Z-force coefficient (i.e., C_(Z), second body-fixed coefficient) based on the determined angle-of-attack parameter. For example, in certain implementations, the determined AOA parameter may be utilized to “look-up” the body Z-force coefficient, C_(Z) (e.g., on a C_(Z) vs. AOA parameter plot (such as FIGS. 5 and 10)) as referenced herein and stored in body Z-force coefficient operating plots 1619). In one implementation, the first and second body-fixed coefficients C_(X) and C_(Z) may be determined through computation of the following equations:

C _(X) =−C _(D) cos α+C_(L) sin α

C _(Z) =−C _(L) cos α−C_(D) sin α

In certain aspects, the lift and drag coefficient values C_(L) and C_(D) (i.e., the aerodynamic data characteristics) in the equations may be measured from wind tunnel data or estimated from aerodynamic data. For example, in certain implementations, with reference to FIG. 7, a monotonic portion 740 of a look-up curve 730 (i.e., a monotonic curve, table look-up; body-fixed accelerations curve) of an angle-of-attack operating plot 700 may be determined (i.e., identified, generated). In some implementations, the trimmed C_(Z) curve 1040 of an body Z-force coefficient operating plot 1000, may be generated prior to an implementation of the method 1500 in any computer either networked to or outside of the computer system 1600, and in other implementations, the trimmed C_(Z) curve 1040 of an body Z-force coefficient operating plot 1000 for a given vehicle may be generated concurrently (i.e., in real-time) in any computer networked to the computer system 1600 as part of the method 1500.

At block 1540, an airspeed value is determined based on the determined second body-fixed load factor measurement (N_(Z)) and the determined body Z-force coefficient (C_(Z)). For example, in certain implementations, an airspeed value (V) may be computed through the following equation:

$v = \left( \frac{2\mspace{14mu} {Nz}\mspace{14mu} ({Weight})}{\rho \mspace{14mu} {Sref}\mspace{14mu} {Cz}} \right)^{\frac{1}{2}}$

In the equation, N_(Z) corresponds to second body-fixed load factor measurement; Weight corresponds to mass*gravity; p corresponds to air density; Sref corresponds to reference wing area; and C_(Z) corresponds to the body Z-force coefficient (i.e., second body-fixed coefficient).

The method 1500 include further steps such as: in response to determining the airspeed value, at least one of: (1) generating, at least partially by a flight computer system, a flight profile of the unpowered vehicle; and (2) adjusting (i.e., correcting), at least partially by the flight computer system (and a closed-loop system), an airspeed setting of the unpowered vehicle.

Advantageously, the computer system 1600 (as described with reference to FIG. 16 below) may generate a flight profile for the vehicle 100. The flight profile may be based on the determined airspeed to: 1) estimate (i.e., calculate) winds to optimize trajectory for vehicle guidance algorithms, 2) serve as an auxiliary system for airspeed, 3) include an optimal AOA for lift-to-drag-optimized angle-of-attack, 4) include the airspeed for an optimal AOA for minimum-sink rate-optimized angle of attack, or a combination thereof. The flight computer system may further adjust (correct for) airspeed (and an angle-of-attack setting) of the unpowered vehicle 100 based on the determined airspeed (and angle-of-attack parameter) such that an associated closed-loop control system may automatically correct the unpowered vehicle in real-time. In addition, both the determined airspeed and/or the determined AOA parameter may also be used in AOA feedback for stability augmentation (i.e., to improve static stability) in a linear range and also may be used as a stall warning. Moreover, the determined airspeed may further be used for table-lookup or gain scheduling.

Moreover, regarding the determined AOA parameter, in certain examples, an operator (e.g., pilot, engineer, aerodynamicist, or flight computer) may evaluate that the determined AOA parameter corresponds to a determined operating point in a sub-optimal region, and thus, the operator may take further actions (such as determining an improved operating point) to bring the AOA of the unpowered vehicle 100 “back” to the optimal AOA.

FIG. 16 is a diagram depicting the computer system 1600 (e.g., networked computer system and/or server) for the example unpowered vehicle 100 (as described in FIG. 1), according to one implementation. FIG. 16 illustrates example hardware components in the computer system 1600 that may be used to determine and/or correct (i.e., adjust) an angle-of-attack parameter (i.e., orientation) for the vehicle 100. The computer system 1600 includes a computer 1610 (e.g., computer, flight computer system, flight controls and avionics computer system), which may be implemented as a server or a multi-use computer that is coupled via a network 1640 to one or more networked (client) computers 1620, 1630. The methods 1400, 1500 may be stored as program code (e.g., AOA optimization program 1624, airspeed program 1626) in memory that may be performed by the computer 1610, the computers 1620, 1630, other networked electronic devices (not shown) or a combination thereof. In some implementations, the AOA optimization program 1624 and the airspeed program 1626 may read input data (e.g., received measurements from the accelerometer 115 and operating plot data of, e.g., respective angle-of-attack and body Z-force coefficient operating plots 1617, 1619) (e.g., as shown in FIGS. 5 and 7 herein) and provide controlled output data to various connected computer systems including an associated closed-loop control system. In certain implementations, each of the computers 1610, 1620, 1630 may be any type of computer, computer system, or other programmable electronic device. Further, each of the computers 1610, 1620, 1630 may be implemented using one or more networked (e.g., wirelessly networked) computers, e.g., in a cluster or other distributed computing system. Each of the computers 1610, 1620, 1630 may be implemented within a single computer or programmable electronic device, e.g., an aircraft flight control computer, a ground-based flight control system, a flight monitoring terminal, a laptop computer, a hand-held computer, phone, tablet, etc. In one example, the computer system 1610 may be an onboard flight control computer (e.g., that is configured to receive accelerometer data from the vehicle 100) on a dispensing aircraft. In such an example, the computer 1620 may be located on the vehicle 100 (e.g., to transmit data from the accelerometer 115 located on the vehicle 100), and the computer 1630 (e.g., that is also configured to receive the accelerometer data from the vehicle 100) may be a part of the computer system 1600 at a ground location monitoring the aircraft and the unpowered vehicle 100.

Advantageously, in example implementations, one or more of the computers 1610, 1620, and 1630 of the flight computer system 1600 may generate a flight profile of the unpowered vehicle 100 and/or adjust (in some instances, automatically) an airspeed configuration (i.e., setting) (and in some implementations, an angle-of-attack (AOA) configuration (i.e., setting)) of the unpowered vehicle 100 based on a determined body Z-force coefficient, C_(Z) and the second body-fixed load factor measurement, N_(Z) (i.e., second accelerometer output) (as well as a determined AOA for the AOA setting) parameter for the of the unpowered vehicle 100.

In one implementation, the computer 1600 includes a central processing unit (CPU) 1612 having at least one hardware-based processor coupled to a memory 1614. The memory 1614 may represent random access memory (RAM) devices of main storage of the computer 1610, supplemental levels of memory (e.g., cache memories, non-volatile or backup memories (e.g., programmable or flash memories)), read-only memories, or combinations thereof. In addition to the memory 1614, the computer system 1600 may include other memory located elsewhere in the computer 1610, such as cache memory in the CPU 1612, as well as any storage capacity used as a virtual memory (e.g., as stored on a storage device 1616 or on another computer coupled to the computer 1610). The memory 1614 may include airspeed and AOA optimization programs 1624, 1626 to determine: a body Z-force coefficient and an AOA parameter of the vehicle 100, and the storage device 1616 may include both respective body Z-force coefficient 1619 and monotonic portions on respective angle-of-attack 1617 operating plots for a variety of different vehicles (to be utilized with the airspeed and AOA optimization programs 1624, 1626) (as described in greater detail with reference to FIGS. 5, 7, 14, and 15). In certain implementations, the airspeed program 1626 may determine optimal airspeed and adjust (e.g., automatically in some instances) airspeed based on the optimal body Z-force coefficient, C_(Z) and measured second body-fixed load factor measurement, N_(Z) utilizing stored body Z-force coefficient operating plots 1619. Moreover, the AOA optimization program 1624 may determine optimal AOA parameters and adjust (e.g., automatically in some instances) AOA configurations based on the optimal AOA parameters utilizing the monotonic portions (e.g., monotonic portion 740) of the stored AOA operating plots 1617.

In FIG. 16, the storage device 1616 is shown to include the stored (monotonic portions on respective) angle-of-attack operating plots 1617 and stored body Z-force coefficient operating plots 1619. In other alternative implementations, (the monotonic portions on respective) the angle-of-attack operating plots 1617 and body Z-force coefficient operating plots 1619 may be stored in the memory 1614, in memory in the computers 1620, 1630, or in any other connected or networked memory storages devices. In some implementations the example monotonic portion for a particular angle-of-attack operating plot and the example body Z-force coefficient operating plot and may be determined in real-time and concurrent with the respective AOA optimization operation 1624 and the airspeed program 1626. In other implementations, the example monotonic portion for a particular angle-of-attack operating plot and the example body Z-force coefficient operating plot and may be determined prior to the respective AOA optimization operation 1624 and the airspeed program 1626.

The computer 1610 may further be configured to communicate information externally. To interface with a user or operator (e.g., aerodynamicist, engineer), the computer 1610 may include a user interface (I/F) 1618 incorporating one or more user input devices (e.g., a keyboard, a mouse, a touchpad, and/or a microphone, among others) and a display (e.g., a monitor, a liquid crystal display (LCD) panel, light emitting diode (LED), display panel, and/or a speaker, among others). In other examples, user input may be received via another computer or terminal. Furthermore, the computer 1610 may include a network interface (I/F) 1615 which may be coupled to one or more networks 1640 (e.g., a wireless network) to enable communication of information with other computers and electronic devices. The computer 1610 may include analog and/or digital interfaces between the CPU 1612 and each of the components 1614, 1615, 1616, and 1618. Further, other non-limiting hardware environments may be used within the context of example implementations.

The computer 1610 may operate under the control of an operating system 1626 and may execute or otherwise rely upon various computer software applications, components, programs, objects, modules, data structures, etc. (such as the AOA optimization program 1624, the airspeed program 1626 and related software). The operating system 1628 may be stored in the memory 1614. Operating systems include, but are not limited to, UNIX® (a registered trademark of The Open Group), Linux® (a registered trademark of Linus Torvalds), Windows® (a registered trademark of Microsoft Corporation, Redmond, Wash., United States), AIX® (a registered trademark of International Business Machines (IBM) Corp., Armonk, N.Y., United States) i5/OS® (a registered trademark of IBM Corp.), and others as will occur to those of skill in the art. The operating system 1626, the AOA optimization program 1624, the airspeed program 1626 in the example of FIG. 16 are shown in the memory 1614, but components of the aforementioned software may also, or in addition, be stored at non-volatile memory (e.g., on storage device 1616 (data storage) and/or the non-volatile memory (not shown). Moreover, various applications, components, programs, objects, modules, etc. may also execute on one or more processors in another computer coupled to the computer 1610 via the network 1640 (e.g., in a distributed or client-server computing environment) where the processing to implement the functions of a computer program may be allocated to multiple computers 1620, 1630 over the network 1640.

Aspects of the present disclosure may be incorporated in a system, a method, and/or a computer program product. The computer program product may include a computer-readable storage medium (or media) having computer-readable program instructions thereon for causing a processor to carry out aspects of the present disclosure. The computer-readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer-readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer-readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer-readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire. For example, the memory 1614, the storage device 1616, or both, may include tangible, non-transitory computer-readable media or storage devices.

Computer-readable program instructions described herein can be downloaded to respective computing/processing devices from a computer-readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in a computer-readable storage medium within the respective computing/processing device.

Computer-readable program instructions for carrying out operations of the present disclosure may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like, and procedural programming languages, such as the “C” programming language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some implementations, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer-readable program instructions by utilizing state information of the computer-readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure.

Aspects of the present disclosure are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the disclosure. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer-readable program instructions.

These computer-readable program instructions may be provided to a processor of a general-purpose computer, a special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus. The machine is an example of means for implementing the functions/acts specified in the flowchart and/or block diagrams. The computer-readable program instructions may also be stored in a computer-readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer-readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the functions/acts specified in the flowchart and/or block diagrams.

The computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to perform a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagrams.

The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various implementations of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in a block in a diagram may occur out of the order noted in the figures. For example, two blocks shown in succession may be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowcharts, and combinations of blocks in the block diagrams and/or flowcharts, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.

In the following description, numerous specific details are set forth to provide a thorough understanding of the disclosed concepts, which may be practiced without some or all of these particulars. In other instances, details of known devices and/or processes have been omitted to avoid unnecessarily obscuring the disclosure. While some concepts will be described in conjunction with specific examples, it will be understood that these examples are not intended to be limiting.

Unless otherwise indicated, the terms “first”, “second”, etc. are used herein merely as labels, and are not intended to impose ordinal, positional, or hierarchical requirements on the items to which these terms refer. Moreover, reference to, e.g., a “second” item does not require or preclude the existence of, e.g., a “first” or lower-numbered item, and/or, e.g., a “third” or higher-numbered item.

Reference herein to “one example” means that one or more feature, structure, or characteristic described in connection with the example is included in at least one implementation. The phrase “one example” in various places in the specification may or may not be referring to the same example.

Illustrative, non-exhaustive examples, which may or may not be claimed, of the subject matter according to the present disclosure are provided below. Different examples of the device(s) and method(s) disclosed herein include a variety of components, features, and functionalities. It should be understood that the various examples of the device(s) and method(s) disclosed herein may include any of the components, features, and functionalities of any of the other examples of the device(s) and method(s) disclosed herein in any combination, and all of such possibilities are intended to be within the scope of the present disclosure. Many modifications of examples set forth herein will come to mind to one skilled in the art to which the present disclosure pertains having the benefit of the teachings presented in the foregoing descriptions and the associated drawings.

Therefore, it is to be understood that the present disclosure is not to be limited to the specific examples illustrated and that modifications and other examples are intended to be included within the scope of the appended claims. Moreover, although the foregoing description and the associated drawings describe examples of the present disclosure in the context of certain illustrative combinations of elements and/or functions, it should be appreciated that different combinations of elements and/or functions may be provided by alternative implementations without departing from the scope of the appended claims. Accordingly, parenthetical reference numerals in the appended claims are presented for illustrative purposes only and are not intended to limit the scope of the claimed subject matter to the specific examples provided in the present disclosure. 

What is claimed is:
 1. A method to determine airspeed of an unpowered vehicle, comprising: during flight, determining, by an accelerometer disposed on the unpowered vehicle, first and second accelerometer outputs, wherein the first and second accelerometer outputs correspond to respective first and second body-fixed load factor measurements; determining an angle-of-attack parameter; determining a body Z-force coefficient based on the angle-of-attack parameter; and determining an airspeed value based on the second body-fixed load factor measurement and the second body-fixed coefficient.
 2. The method of claim 1, further comprising, in response to determining the airspeed value, at least one of: generating, at least partially by a flight computer system, a flight profile of the unpowered vehicle; and adjusting, at least partially by the flight computer system, an airspeed setting of the unpowered vehicle based on the airspeed value.
 3. The method of claim 1, wherein the angle-of-attack parameter is determined based on one of direct measurement or computation, wherein determining the angle-of-attack parameter by computation comprises: determining a monotonic portion of a look-up curve of an angle-of-attack operating plot; determining an operating point on the monotonic portion by applying a quotient of the first and second accelerometer outputs to the angle-of-attack operating plot; and determining the angle-of-attack parameter corresponding to the determined operating point.
 4. The method of claim 3, wherein determining the operating point on the monotonic curve portion by applying the quotient of the first and second accelerometer outputs to the angle-of-attack operating plot comprises: matching a quotient of the first and second accelerometer outputs to a substantially equivalent body-fixed acceleration, wherein the body-fixed acceleration corresponds to a particular quotient of a particular first and second body-fixed coefficients, and wherein the particular quotient of the first and second body-fixed coefficient corresponds to a particular respective first and second aerodynamic data characteristic.
 5. The method of claim 4, wherein the particular respective first and second aerodynamic data characteristic corresponds to a particular respective lift coefficient metric and drag coefficient metric.
 6. The method of claim 3, wherein the monotonic curve portion corresponds to a plurality of body-fixed accelerations as a function of a plurality of angle-of-attack parameters.
 7. The method of claim 6, wherein the plurality of angle-of-attack parameters corresponds to a respective range of prospective angle-of-attack directions.
 8. The method of claim 7, wherein the angle-of-attack parameter of the plurality of angle-of-attack parameters corresponds to one direction of the range of the prospective angle-of-attack directions, and wherein the angle-of-attack parameter corresponds to a lift-to-drag-optimized angle-of-attack, a minimum-sink rate-optimized angle of attack, or a combination thereof.
 9. The method of claim 6, wherein the plurality of body-fixed accelerations corresponds to a quotient of the pluralities of first and second body-fixed coefficients.
 10. The method of claim 9, wherein the plurality of a first body-fixed coefficient is based on a corresponding plurality of a first aerodynamic data characteristic and a range of angle-of-attack directions.
 11. The method of claim 10, wherein the plurality of a first aerodynamic data characteristic comprises a plurality of lift coefficient metrics.
 12. The method of claim 9, wherein the plurality of a second body-fixed coefficient is based on a corresponding plurality of a second aerodynamic data characteristic and a range of angle-of-attack directions.
 13. The method of claim 12, wherein the plurality of a second aerodynamic data characteristic comprises a plurality of drag coefficient metrics.
 14. The method of claim 3, wherein the operating point corresponds to a particular body-fixed acceleration as function of a corresponding particular angle-of-attack parameter.
 15. The method of claim 3, wherein determining the monotonic portion of the look-up curve of the angle-of-attack operating plot comprises: obtaining pluralities of first and second aerodynamic data characteristics as respective functions of a range of angle-of-attack directions; computing, by a processor, pluralities of first and second body-fixed coefficients as the respective functions of the range of angle-of-attack directions; determining, by the processor, a plurality of body-fixed accelerations as a function of a prospective range of the range of angle-of-attack directions based on respective pluralities of quotients of the first and second body-fixed coefficients as the respective functions of the range of angle-of-attack directions, wherein the determined plurality of body-fixed accelerations as a function of a prospective range of the range of angle-of-attack directions corresponds to the look-up curve of the angle-of-attack operating plot; and determining the monotonic portion based on a filtering, by the processor, of the look-up curve.
 16. The method of claim 15, wherein the pluralities of first and second aerodynamic data characteristics are obtained by estimating the range of the body-fixed accelerations for the vehicle or by measuring wind tunnel data with respect to the vehicle.
 17. The method of claim 15, wherein the monotonic portion comprises a portion of the look-up curve corresponding to decreasing values of the determined plurality of body-fixed accelerations as a function of increasing degrees of the prospective range of the range of angle-of-attack directions.
 18. The method of claim 1, wherein the first body-fixed load factor measurement corresponds to a quotient of a magnitude of axial force and weight, and wherein the second body-fixed load factor measurement corresponds to a quotient of a magnitude of normal force and weight.
 19. A flight computer system comprising: a processor; and a memory accessible to the processor, the memory storing instructions that are executable by the processor to perform operations comprising: during flight, determining, by an accelerometer disposed on the unpowered vehicle, first and second accelerometer outputs, wherein the first and second accelerometer outputs correspond to respective first and second body-fixed load factor measurements; determining an angle-of-attack parameter; determining a body Z-force coefficient based on the angle-of-attack parameter; and determining an airspeed value based on the second body-fixed load factor measurement and the second body-fixed coefficient.
 20. A non-transitory computer-readable storage device storing instructions that, when executed by a processor, cause the processor to: during flight, determining, by an accelerometer disposed on the unpowered vehicle, first and second accelerometer outputs, wherein the first and second accelerometer outputs correspond to respective first and second body-fixed load factor measurements; determining an angle-of-attack parameter; determining a body Z-force coefficient based on the angle-of-attack parameter; and determining an airspeed value based on the second body-fixed load factor measurement and the second body-fixed coefficient. 